Description: Obsolete version of ssexg as of 18-Jul-2026. (Contributed by NM, 14-Aug-1994) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ssexgOLD | |- ( ( A C_ B /\ B e. C ) -> A e. _V ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseq2 | |- ( x = B -> ( A C_ x <-> A C_ B ) ) |
|
| 2 | 1 | imbi1d | |- ( x = B -> ( ( A C_ x -> A e. _V ) <-> ( A C_ B -> A e. _V ) ) ) |
| 3 | vex | |- x e. _V |
|
| 4 | 3 | ssex | |- ( A C_ x -> A e. _V ) |
| 5 | 2 4 | vtoclg | |- ( B e. C -> ( A C_ B -> A e. _V ) ) |
| 6 | 5 | impcom | |- ( ( A C_ B /\ B e. C ) -> A e. _V ) |